The Voyager probes have a scan platform, which allowed them to point their cameras independently of the orientation of the spacecraft. New Horizons doesn't have a scan platform, so the entire spacecraft must be rotated to point the cameras in the right direction. As a result, the mission planners had to choose between observations and downlinking data at several points during the Pluto flyby.
Why wasn't a scan platform included in New Horizons?
PS: The reason I've asked this question: a couple of recent questions here are about Pluto encounter planning. The answers usually refer to NH's lack of a scan platform, but we haven't tackled the underlying reason yet.